API

DotsNotation <: RepeatingDecimalNotation

A type to represent a repeating decial with parentheses notation like "0.1(6)".

julia> rd"123.456̇78̇"
4111111//33300

julia> no = DotsNotation()
DotsNotation()

julia> stringify(no, 1//11)
"0.0̇9̇"

julia> rationalify(no, "123.456̇78̇")
4111111//33300

EllipsisNotation <: RepeatingDecimalNotation

A type to represent a repeating decial with ellipsis notation like "0.1666...".

julia> rd"123.45678678..."
4111111//33300

julia> no = EllipsisNotation()
EllipsisNotation()

julia> stringify(no, 1//11)
"0.0909..."

julia> rationalify(no, "123.45678678...")
4111111//33300

julia> rd"0.4545..."      # Same as 0.(45), repeating [45] two times
5//11

julia> rd"0.333..."       # Same as 0.(3), repeating one digit [3] three times
1//3

julia> rd"0.13331333..."  # Same as 0.(1333), repeating [1333] has priority over repeating [3]
1333//9999

julia> rd"0.133313333..." # Same as 0.13331(3), adding additional [3] resolves the ambiguity.
19997//150000

ParenthesesNotation <: RepeatingDecimalNotation

A type to represent a repeating decial with parentheses notation like "0.1(6)".

julia> rd"123.45(678)"
4111111//33300

julia> no = ParenthesesNotation()
ParenthesesNotation()

julia> stringify(no, 1//11)
"0.(09)"

julia> rationalify(no, "123.45(678)")
4111111//33300

RepeatingDecimal

Intermediate struct to represent a repeating decimal number.

Examples

julia> RepeatingDecimal(false, 12743, 857142, 2, 6)
       2|--|------|6
    -127.43(857142)
----------- --------------
Finite part Repeating part

julia> RepeatingDecimal(1//17)
         0||----------------|16
        +0.(0588235294117647)
----------- -------------------
Finite part Repeating part

Abstract supertype for repeating decimals notations.

ScientificNotation <: RepeatingDecimalNotation

A type to represent a repeating decial with scientific notation like "0.1r6".

julia> rd"123.45r678"
4111111//33300

julia> no = ScientificNotation()
ScientificNotation()

julia> stringify(no, 1//11)
"0.r09"

julia> rationalify(no, "123.45r678")
4111111//33300

julia> rd"1.2345r678e2"  # Exponent term is supported.
4111111//33300

rationalify(::Type{<:Integer}, ::RepeatingDecimalNotation, ::AbstractString)
rationalify(::Type{<:Integer}, ::RepeatingDecimal)
rationalify(::Type{<:Integer}, ::AbstractString)
rationalify(::RepeatingDecimalNotation, ::AbstractString)
rationalify(::RepeatingDecimal)
rationalify(::AbstractString)

Generate String from Rational or RepeatingDecimal instance.

Examples

julia> using RepeatingDecimalNotations: rationalify  # `rationalify` is not exported.

julia> rationalify(RepeatingDecimal(true, 123, 45, 2, 3))  # `RepeatingDecimal` to `Rational{Int}`
6829//5550

julia> rationalify("1.23r045")  # `String` to `Rational{Int}`
6829//5550

julia> rationalify(EllipsisNotation(), "1.23r045")  # If notation style is specified, the input string should follow the style.
ERROR: invalid input!
Stacktrace:
[...]

julia> rationalify(Int128, "1.23r045")  # `String` to `Rational{Int128}`
6829//5550

julia> typeof(ans)
Rational{Int128}

stringify(::RepeatingDecimalNotation, ::RepeatingDecimal)
stringify(::RepeatingDecimalNotation, ::Rational)
stringify(::RepeatingDecimal)
stringify(::Rational)

Generate String from Rational or RepeatingDecimal instance.

Examples

julia> using RepeatingDecimalNotations: stringify  # `stringify` is not exported.

julia> stringify(ScientificNotation(), RepeatingDecimal(true, 123, 45, 2, 3))
"1.23r045"

julia> stringify(EllipsisNotation(), 1//11)
"0.0909..."

julia> stringify(RepeatingDecimal(true, 123, 45, 2, 3))  # Defaults to `ParenthesesNotation()`.
"1.23(045)"

julia> stringify(1//11)
"0.(09)"

@rd_str

A string macro to create a rational number.

Examples

julia> r = rd"123.4(56)"  # 123.4565656...
61111//495

julia> rd"1.234r56e2"  # Other notations
61111//495

julia> rd"123.45656..."  # are also supported.
61111//495

julia> float(r)  # Check floating point number approximation.
123.45656565656566

julia> rd"0.(9)"  # 0.999... is equal to 1.
1//1

julia> rd"0.99(9)", rd"1", rd"1.000_000"  # The notation of repeating decimals is not unique.
(1//1, 1//1, 1//1)